
The corresponding real time magnetic sensitivity defined in Ref. [1]} is approximately equal to \(10^{-19}\mathbf {T} Hz^{-1/2} \) . It is six orders of magnitude higher than that of the state-of-the-art magnetoelectric sensors [1]}. The estimated magnetic sensitivity can approach \(10^{-15} Hz^{-1/2}\)  in the Ref. [3]}. But it needs the strong coupling region \(g\gg \kappa \) . As a contrast, our scheme only requires the week coupling, which is more easily in experiment [4]}.
